Right here’s a well-known teaser that I don’t actually like a lot: What quantity comes subsequent within the sequence 8, 5, 4, 9, 1, 7,…? It’s not so apparent. It turns into a bit simpler once we write the sequence in phrases: eight, 5, 4, 9, one, seven, …. Spot it now? The reply is 6, as a result of the digits are given in alphabetical order (and 6 comes subsequent). It’s a high-quality trick, but it surely preys on the forgivable assumption {that a} sample in a sequence of numbers may have one thing to do with numbers. I choose when the parameters of a puzzle are clear. There are lots of neat observations we are able to make once we view numbers as phrases—no deception required. Strive answering the questions under to see what I imply.
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Did you miss final week’s puzzle? Test it out right here, and discover its answer on the backside of at the moment’s article. Watch out to not learn too far forward if you happen to haven’t solved final week’s but!
Puzzle #15: Spell It Out
What’s the smallest quantity that comprises the letter “a” when spelled out?There is just one quantity that, when spelled out, has its letters in alphabetical order. What’s it? There may be additionally just one quantity with its letters in reverse alphabetical order. What’s it? Think about we fill a dictionary with the primary trillion numbers in alphabetical order. What’s the first odd quantity within the dictionary? This query is harder than it sounds!
Some clarifications:
We’re solely contemplating the counting numbers 1, 2, 3, 4, and so on. No fractions, decimals, or negatives.We’re spelling numbers in a canonical means that doesn’t use the phrase “and.” For instance, the quantity 426 is written “4 hundred twenty six.” The quantity 2,500 should be written “two thousand 5 hundred” and can’t be written as “twenty 5 hundred.” 25,000 alternatively is written “twenty 5 thousand.” 100 is written “100” and never “100.” Ignore all hyphens and areas. For instance, sixteen comes earlier than six thousand.
Whereas a few of these may sound like workouts in brute drive search, there are strategic methods that you would be able to trim down the search area. Discover the patterns in how we identify our numbers and take a stab at whichever immediate you discover essentially the most compelling.
If of some other quirky properties of spelled out numbers, please share them within the feedback.
I’ll be again subsequent Monday with the answer and a brand new puzzle. Are you aware a cool puzzle that I ought to cowl right here? Ship it to me at [email protected]
Answer to Puzzle #14: Elon Musk’s Interview Query
Did you make progress on final week’s puzzle, or did it have you ever strolling in circles? Apart from the North Pole, there are literally infinitely many various options. Bear in mind to think about strains of latitude really as circles across the planet that get progressively narrower close to the poles. Image the circle of latitude close to the South Pole that’s precisely 1 mile lengthy. The important thing statement is that, since this circle is 1 mile, strolling west 1 mile alongside it sends you all the best way round and again to the place you started. So an alternate answer to the puzzle is any level that lies a mile north of this circle. Strolling one mile south from there places you on the circle. One mile west then loops you completely across the circle, not having modified your place in any respect, after which the ultimate mile north brings you again as much as your place to begin.
We will prolong this concept additional. Image a smaller ring even nearer to the South Pole the place the circle of latitude is precisely half a mile lengthy. Strolling 1 mile west alongside this circle will ship you two laps round after which settle you the place you began. So any level precisely 1 mile north of this circle works as nicely. This provides us an entire household of options: the entire factors precisely 1 mile north of the circle of latitude close to the South Pole measuring ⅓ of a mile, and the identical for the circle measuring ¼ of a mile, and so forth.